Gibbs Free Energy, Maxwell Relations

[albertov123]

Homework Statement

We have a Gibbs Free Energy function G=G(P, T, N₁, N₂) I am not writing the whole function because I just want a push in the right direction. Find expressions for the entropy, volume, internal energy, enthalpy and chemical potential.

Homework Equations

Maxwell Relations
T=(dU/dS) V and N_i constant
-P=(dU/dV) S and N_i constant
T=(dH/dS) P and N_i constant
V=(dH/dP) S and N_i constant

The Attempt at a Solution

I have found entropy, volume and chemical potential (partial molar gibbs free energy) functions using related equations. But I'm not sure on how to derive internal energy and enthalpy expressions.
If I try to make use of above equations, for an example first equation dU=TdS so U=T.dS
but also from second equation dU=-PdV so U=-PdV

Can both be correct at the same time? I think they would yield different equations.

If I am going absolutely wrong, do you have any idea on how to find U and H expressions. What other relations could be used?

 

[Chestermiller]

For H, start with dG=-SdT-VdP+μ₁dN₁+μ₂dN₂, and substitute S=(H-G)/T. Then consider dP=0, dN's = 0.